Does Linux take kindly to being installed on one computer and then taken an put in another computer?

I already transplanted my Slack10 as a way to test a new computer. I had a harddisk with WinXP and Slack10 on it. WinXP wouldn't boot at all, but Slack started right up. I had just got a new computer, and was only allowed to start it up and test it to make sure everything worked before it got packed away for christmas.

The sound didn't work right. I ran alsaconf and setup the onboard audio, but trying to play an mp3 with amp only played the first second or so before stuttering and stopping. Amp didn't crash, but the sound stopped. The nVidia driver didn't work right either. After installing it and starting up KDE, the desktop was all jacked up. It didn't refresh at all, and old menus stayed on screen after they were closed. glxgears ran at like a million fps, so I guess the 3daccel is working. Those were the only problems I noticed, but I only got to use it for a little while.

I think I might have made a custom kernel (that'll probably do it), but I don't know. Whould the transplant have caused these problems?

Generally linux will transplant fine, you will however, need to do some configuration, i.e. sound, video, nic, etc. The more stock the kernel, the better the chances of things working.
good luck.

I have had that problem before, and the solution was (for me anyway) to adjust my DMA and IRQ settings for the module.